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The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
A random surface scattering in a one-mode waveguide is studied in the case when the surface profile has long-range correlations along the waveguide. Analytical treatment of this problem shows that with a proper choice of the surface, one…
Evanescently coupled waveguides are a powerful platform to study and visualize the wave dynamics in tight-binding systems. Here, we investigate the propagation of surface plasmon polaritons in arrays of dielectric loaded surface plasmon…
We derive a new approach to analyze the coupling of linear Boussinesq and Saint-Venant shallow water wave equations in the case where the interface remains at a constant position in space. We propose a one-way coupling model as a reference,…
This is a continuation of the authors' previous work (A. Kirsch, Math. Meth. Appl. Sci., 45 (2022): 5737-5773.) on well-posedness of time-harmonic scattering by locally perturbed periodic curves of Dirichlet kind. The scattering interface…
Coexisting periodic solutions of a dynamical system describing nonlinear optical processes of the second-order are studied. The analytical results concern both the simplified autonomous model and the extended nonautonomous model, including…
This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\varepsilon$. The small parameter $\varepsilon>0$ denotes the…
In this paper we study the long time behavior for a semilinear wave equation with space-dependent and nonlinear damping term. After rewriting the equation as a first order system, we define a class of approximate solutions that employ…
An analytical method for the visualization and prediction of trapped-mode resonances based on the dimensions of a dispersive microwave network is described. The method as explained is intuitive, easy to implement, and has proven itself to…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
We study the number of propagating Bloch modes N_B of an infinite periodic billiard chain. The asymptotic semiclassical behavior of this quantity depends on the phase-space dynamics of the unit cell, growing linearly with the wavenumber k…
We study the dynamics of an electron subjected to a static uniform electric field within a one-dimensional tight-binding model with a slowly varying aperiodic potential. The unbiased model is known to support phases of localized and…
An analysis is presented of frequency versus wave-vector dispersion in elliptically birefringent one-dimensional layered periodic structures. The presence of local normal mode polarization state variations from one layer to the next is…
Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction…
Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…
The interaction between three localized vibrational modes is shown to be as relevant for the lifetimes of localized modes as the interaction involving two localized and one extended, and one localized and two extended modes. This contrasts…
We study numerically the cubic-quintic-septic Swift-Hohenberg (SH357) equation on bounded one-dimensional domains. Under appropriate conditions stripes with wave number $k\approx 1$ bifurcate supercritically from the zero state and form…
The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In oceanography it is known as the Alber equation, and its…
We numerically investigate the light beam propagation in periodic waveguide arrays which are elaborately modulated with certain structures. We find that the light beam may split, coalesce, deflect, and be localized during propagation in…